Rated 4 out of 5 stars

These aren't emoji, they're images. Emoji are letters and should rely on font for display.

Edit: Fair enough. (see answer below)

This review is for a previous version of the add-on (1.5.4). 

In HTML mode you can Shift-click to insert the Unicode character only. Even though by default in HTML mode images are inserted, the alt attribute of the inserted image is set to the Unicode character so if you copy the emoji the Unicode character will be on the clipboard. In plaintext mode the Unicode character is always only inserted.